I'm not qualified to even have an opinion on this but that aside, Consistent Histories is my favorite QM interpretation. I think any interpretation that includes FTL or cannot even recover the predictions of QFT is deeply flawed..
Discussion
I like that there is no wavefunction collapse and that measurement isn't special, and that observers are not special. It's also interesting that it avoids non-locality, and appears to actually measure pre-existing hidden variables... all kinds of things that were supposedly proven wrong already.
The problem is that probabilistic statements made about two things that belong to different decoherent families are simply forbidden, claimed to be meaningless questions. That's either a brilliant insight explaining precisely our misunderstanding of reality and probability, or else it is a total logical contradiction and completely dumb. And I can't tell which it is, but I'm leaning towards completely dumb.